Simplify (1+i)^3

${(1 + i)}^{3}$

Step 1

Use the Binomial Theorem.

$1^{3} + 3 \cdot 1^{2} i + 3 \cdot 1 i^{2} + i^{3}$

Step 2

Simplify terms.

Simplify each term.

One to any power is one.

$1 + 3 \cdot 1^{2} i + 3 \cdot 1 i^{2} + i^{3}$

One to any power is one.

$1 + 3 \cdot 1 i + 3 \cdot 1 i^{2} + i^{3}$

Multiply $3$ by $1$ .

$1 + 3 i + 3 \cdot 1 i^{2} + i^{3}$

Multiply $3$ by $1$ .

$1 + 3 i + 3 i^{2} + i^{3}$

Rewrite $i^{2}$ as $- 1$ .

$1 + 3 i + 3 \cdot - 1 + i^{3}$

Multiply $3$ by $- 1$ .

$1 + 3 i - 3 + i^{3}$

Factor out $i^{2}$ .

$1 + 3 i - 3 + i^{2} \cdot i$

Rewrite $i^{2}$ as $- 1$ .

$1 + 3 i - 3 - 1 \cdot i$

Rewrite $- 1 i$ as $- i$ .

$1 + 3 i - 3 - i$

$1 + 3 i - 3 - i$

Simplify by adding terms.

Subtract $3$ from $1$ .

$- 2 + 3 i - i$

Subtract $i$ from $3 i$ .

$- 2 + 2 i$

$- 2 + 2 i$

$- 2 + 2 i$

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